Question

Find the nth term formula for the arithmetic sequence if a12=212, a34=652

Answer 1

The n-th term formula is
\[\large a_n=a_1+(n-1)d \]
So you need to find \(a_1\) and \(d\).

\(\large a_{12}=212=a_1+(12-1)d\\
\large a_{34}=625=a_1+(34-1)d\)

You thus have a system of equations with 2 unknowns and 2 equations, so you can solve for \(a_1\) and \(d\)